Max Born and the quantum theory

American Journal of Physics

Volumn 73, Issue 11, 2005, Pages 999-1008

  Bernstein, Jeremy ^a  

^a Stevens Institute of Technology   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 27744441917     PISSN: 00029505     EISSN: None     Source Type: Journal    
DOI: 10.1119/1.2060717     Document Type: Review

References (46)

1. Some of the more notable biographies include the following: Albrecht Fölsing, Albert Einstein (Penguin Books, New York, 1998);
2. Abraham Pais, Niels Bohr's Times (Oxford University Press, New York, 1991);
3. Walter J. Moore, Schrödinger, Life and Thought (Cambridge University Press, New York, 1992);
4. Abraham Pais, Maurice Jacob, David I. Olive, and Michael F. Atiyah, Paul Dirac: The Man and His Work (Cambridge University Press, New York, 2005);
5. David C. Cassidy, Uncertainty; The Life and Science of Werner Heisenberg (W. H. Freeman and Co., New York, 1992).
6. The play in question is Michael Frayn, Copenhagen (Anchor Books, New York, 2001).
7. Nancy Thorndike Greenspan, The End of a Certain World (Basic Books, New York, 2005).
8. Reference 1, p. 144.
9. Reference 1, p. 2.
10. Barbara Goldsmith, Obsessive Genius: The Inner World of Marie Curie (Atlas Books, W. W Norton & Company, New York, 2005).
11. Goldsmith does not seem to understand that krypton was also produced in the fission whose mass Meitner had to know.
12. Reference 4, p. 225.
13. Reference 1, p. 62.
14. For a wonderful view of Göttingen see John Derbyshire, Prime Obsession (Joseph Henry Press, Washington, DC, 2003). In contrast to the two books I have mentioned, Derbyshire's book, which concerns Riemann's hypothesis about the zeros of the Riemann function, is a model of how a popular science book should be written.
15. This quote is from Constance Reid, Hilbert (Springer, New York, 1996).
16. The Born-Einstein Letters: Friendship, Politics and Physics in Uncertain Times, with an introduction by Kip Thorne and Diana Buchwald (Mc-Millan, New York, 2005).
17. Reference 1, p. 61. The italics are mine.
18. A. Einstein, "Strahlungs-Emission und -Absorption nach der Quantentheorie," Verh. Dtsch. Phys. Ges. 18, 318 (1916).
19. A good account can be found in David Bohm, Quantum Theory (Dover, New York, 1989). Bohm compares the answer found in this way with the real quantum mechanical answer and shows that at least in simple cases they agree surprisingly well.
20. A account of this chronology can be found in David Cassidy, Uncertainty; The Life and Science of Werner Heisenberg (W. H. Freeman, New York, 1992).
21. I have been greatly helped by two papers that I would suggest reading in the following order. First, William A. Fedak and Jeffery J. Prentis, "Quantum jumps and classical harmonics," Am. J. Phys. 70(3), 332-344 (2002); and
22. Ian J. R. Aitchison, David A. MacManus and Thomas M. Snyder, "Understanding Heisenberg's 'magical' paper of July 1925: A new look at the calculational details," Am. J. Phys. 72(11), 1370-1379 (2004);
23. A translation of the original paper can be found in Sources of Quantum Mechanics, edited by B. L. van der Waerden (Dover, New York, 1967), pp. 261-276.
24. See van der Waerden, Ref. 13, p. 261.
25. Here and in what follows I will ignore the following subtlety. In general these transition amplitudes are complex numbers and the squares are absolute values squared. For purpose of this review I will treat them as if they were real numbers. This will not affect anything.
26. Reference 1, p. 125.
27. See van der Waerden, Ref. 13, p. 266.
28. For a discussion see Marshall Bowen, and James Coster, "Born's discovery of the quantum-mechanical matrix calculus," Am. J. Phys. 48(6), 491-492 (1980).
29. These are clearly spelled out in Aitchison et al., Ref. 13, Appendix A.
30. 2.
31. See van der Waerden, Ref. 13, p. 40.
32. Most of it is reproduced in translation in van der Waerden, Ref. 13. For reasons that are unclear van der Waerden leaves out the last few pages of the original which Jordan later complained about.
33. Van der Waerden, Ref. 13, p. 277.
34. I am grateful to Helmut Rechenberg for remarks on Jordan's career and other points in my review.
35. This full text of this and many other wartime pronouncements of German scientists can be found in Physics and National Socialism, edited by Klaus Hentschel (Birkhäuser, Boston, 1996), p. 272.
36. I am grateful to Peter Goddard for supplying this and for his comments.
37. Later in 1926, Dirac published a second paper in which he used matrix methods to discuss the hydrogen atom. See P. A. M. Dirac, "Quantum mechanics and a preliminary investigation of the hydrogen atom," Proc. R. Soc. London, Ser. A 110, 561 (1926)]. In this paper he does refer to Born and Jordan.
38. Reference 1, p. 191
39. M. Born, "Zur Quantenmechanik der Stoßvorgänge," Z. Phys. 37, 863-867 (1926);
40. "Quantenmechanik der Stoßvorgänge," Z. Phys. 38, 803-827 (1926).
41. One again I am ignoring the fact that these functions are in general complex numbers so that you must take the absolute value squared.
42. This quotation can be found in Abraham Pais, Subtle is the Lord (Oxford University Press, New York, 1982), p. 442. The first bracket is mine and the other two are Pais's.
43. Reference 30, p. 443
44. See M. Born, "The statistical interpretation of quantum mechanics," in Nobel Lectures in Physics 1942-1962 (Elsevier, Amsterdam, 1964).
45. Reference 1, p. 159
46. M. Born and L. Infeld, "Foundations of the new field theory," Proc. R. Soc. London, Ser. A 144, 425-451 (1934).